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28 April, 2009

Algebraic Representation- Applications of pair of linear equations in two variables

Q.1-Aftab tells his duaghter,"seven years ago,I was seven times as old as you were then.Also three years from now,I shall be three times as old as you will be."Represent this situation algebrically" .
Solution :Let the age of Aftab be x years.and the age of his daughter be y years.
7 years ago... Age of Aftab = x-7 years , Age of his daughter = y-7 years
According to given condition
(x-7) = 7(y-7)
=>x-7y=-42 --------(1)
3 years later....Age of Aftab = x+3 years , Age of his daughter = y+3 years
According to given condition
(x+3) = 3( y+3)
=> x+3 = 3y+9
=>x-3y=6 ---------(2)


Q.2-The coach of a cricket team buys 3 bats & 6 balls for Rs.3900.Later,she buys 1 bat & 2 more balls of the same kind for Rs.1300.Represent this situation algebrically .
Solution:
Let the cost of bats be Rs.x
and the cost of balls be Rs.y.
According to given conditions:-
3x+6y=3900 and
x+3y=1300
Q.3-The cost of 2kg of apples & 1kg of grapes on a day was found to be Rs.160.After a month, cost of 4kg of apples & 2kg of grapes is Rs.300. Represent this situation algebrically.

Solution:
Let the cost of 1 Kg of apples be Rs.x
and the cost of 1 Kg of grapes be Rs.y
According to given conditions:-
2x+y=160 and
4x+2y=300

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